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For non-empty topological spaces X and Y and arbitrary families $𝒜$ ⊆ $𝒫 (X)$ and $ℬ \subseteq 𝒫 (Y)$ we put $𝒞_{𝒜, ℬ}$ =f ∈ $Y^{X}$ : (∀ A ∈ $𝒜$ )(f[A] ∈ $ℬ)$ . We examine which classes of functions $ℱ$ ⊆ $Y^{X}$ can be represented as $𝒞_{𝒜, ℬ}$ . We are mainly interested in the case when $ℱ = 𝒞 (X, Y)$ is the class of all continuous functions from X into Y. We prove that for a non-discrete Tikhonov space X the class $ℱ = 𝒞$ (X,ℝ) is not equal to $𝒞_{𝒜, ℬ}$ for any $𝒜$ ⊆ $𝒫 (X)$ and $ℬ$ ⊆ $𝒫$ (ℝ). Thus, $𝒞$ (X,ℝ) cannot be characterized by images of sets. We also show that none of the following classes of...

Functor of extension in Hilbert cube and Hilbert space

Piotr Niemiec (2014)

Open Mathematics

It is shown that if Ω = Q or Ω = ℓ 2, then there exists a functor of extension of maps between Z-sets in Ω to mappings of Ω into itself. This functor transforms homeomorphisms into homeomorphisms, thus giving a functorial setting to a well-known theorem of Anderson [Anderson R.D., On topological infinite deficiency, Michigan Math. J., 1967, 14, 365–383]. It also preserves convergence of sequences of mappings, both pointwise and uniform on compact sets, and supremum distances as well as uniform continuity,...

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Full embeddings with a given restriction

Function spaces and adjoints.

Functional separation of inductive limits and representation of presheaves by sections. Part IV: Representation of presheaves by sections

Functional separation of inductive limits and representation of presheaves by sections. Part II. Embedding of presheaves into presheaves of compact spaces

Functional separation of inductive limits and representation of presheaves by sections. Part III: Some special cases of separation of inductive limits of presheaves

Functional separation of inductive limits and representation of presheaves by sections. Part one: Separation theorems for inductive limits of closured presheaves

Functionally Hausdorff spaces

Functions characterized by images of sets

Functor of extension in Hilbert cube and Hilbert space

Functorial algebras and automata

Functorial and algebraic properties of Browns $𝒫$ functor.

Functorial approximation to the lateral completion in archimedean lattice-ordered groups with weak unit

Functorial concepts of complexity for finite automata.

Functorial polymorphism and semantic parametricity

Functorial prolongations of Lie groups and their actions

Functorial properties of the lattice of functional semi-norms.

Functorial rings of quotients 2: the ring of hyper-fractions.

Functors on locally finitely presented additive categories

Fundamental groupoids of $k$ -graphs.

Fundamental Groups, Algebraic K-Theory, and a Problem of Abhyankar.

Currently displaying 101 – 120 of 126